February

February 1 – New York City's Grand Central Terminal, having been rebuilt, reopens as the world's largest railroad station.

February 3 – The 16th Amendment to the United States Constitution is ratified, authorizing the Federal government to impose and collect income taxes.

February 9 – Mexican Revolution: Beginning of La Decena Trágica, the rebellion of some military chiefs against the President Francisco I. Madero.

February 18 – Mexican Revolution: President Francisco I. Madero and Vice President José María Pino Suárez are forced to resign. Pedro Lascuráin serves as President for less than an hour before General Victoriano Huerta, leader of the coup, takes office

The U.S. Department of Commerce and U.S. Department of Labor are established by splitting the duties of the 10-year-old Department of Commerce and Labor. The Census Bureau, U.S. Bureau of Fisheries and U.S. Coast and Geodetic Survey form part of the Department of Commerce.

April

April 8 – The Seventeenth Amendment to the United States Constitution is passed, dictating the direct election of senators.

April 21 – Cunard ocean liner RMS Aquitania, built by John Brown & Company, is launched on the River Clyde.

May

May 3 – Raja Harishchandra, the first full-length Indian feature film is released, marking the beginning of the Indian film industry.

May 13 – Igor Sikorsky becomes the first person to pilot a 4-engine aircraft.

May 14 – New York Governor William Sulzer approves the charter for the Rockefeller Foundation, which begins operations with a $100,000,000 donation from John D. Rockefeller.

May 29 – The balletThe Rite of Spring, with music by Igor Stravinsky conducted by Pierre Monteux, choreography by Vaslav Nijinsky and design by Nicholas Roerich, is premièred by Sergei Diaghilev's Ballets Russes at the Théâtre des Champs-Élysées in Paris; its modernism provokes one of the most famous classical music riots in history.

May 30 – First Balkan War: The Treaty of London is signed, ending the war. Greece is granted those parts of southern Epirus which it does not already control.

June

June 1 – The Greek-Serbian Treaty of Alliance is signed, paving the way for the Second Balkan War.

June 4 – Emily Davison, a British suffragette, runs out in front of the King's horse, Anmer, at the Epsom Derby. She is trampled and dies 4 days later in hospital, never having regained consciousness.

June 8 – The Deutsches Stadion in Berlin is dedicated with the release of 10,000 pigeons in front of an audience of 60,000 people. It had been constructed in anticipation of the 1916 Summer Olympics, later to be cancelled the result of World War I.

June 11 – Battle of Bud Bagsak: Armed with guns and heavy artillery, U.S. and Philippine troops under General John J. "Black Jack" Pershing fight a four-day battle against 500 Moro rebels who are armed mostly with kampilan swords. The rebels are killed in a final desperate charge on June 15.

June 18 – The Arab Congress of 1913 opens, during which Arab nationalists meet to discuss desired reforms under the Ottoman Empire.

June 19 – The Parliament of South Africa forbids blacks from owning or buying land from whites.

July

Death Valley, California hits 134 °F (~56.7 °C), the highest temperature recorded in the world (as of 2012).

July 27 – Foundation of the town of San Javier, Uruguay, by Russian settlers.

August

August 4 – In China, the province of Chungking declares independence; Chinese Republican forces crush the rebellion in a couple of weeks.

August 10 – Second Balkan War: The Treaty of Bucharest is signed, ending the war. Macedonia is divided and Northern Epirus is assigned to Albania.

August 13 – Invention of stainless steel by Harry Brearley in Sheffield.

August 20 – After his airplane failed at an altitude of 900 feet (270 m), aviator Adolphe Pegoud became the first person to bail out to safety from an airplane and to land safely.

August 26 – Dublin Lock-out in Ireland: Members of James Larkin's Irish Transport and General Workers' Union employed by the Dublin United Tramways Company begin strike action in defiance of the dismissal of trade union members by its chairman.

August 31 – Dublin Lock-out: "Bloody Sunday": The dispute escalates when the Dublin Metropolitan Police kill one demonstrator and injure 400 in dispersing a demonstration.

September

The Balkan boundaries after 1913

September 9 – In Germany, BASF starts the world's first plant for the production of fertilizer based on the Haber-Bosch process, feeding today about a third of the world's population.

September 17 – In Chicago, the Anti-Defamation League of B'nai B'rith is founded, with Sigmund Livingston as its first president.

September 23 – French aviator Roland Garros crosses the Mediterranean in an airplane flying from Fréjus, France to Bizerte, Tunisia.

September 29 – Second Balkan War: The Treaty of Constantinople is signed in Istanbul between the Ottoman Empire and the Kingdom of Bulgaria.

October

October 1 – Mexican Revolution: Pancho Villa's troops take Torreón after a 3-day battle, when government troops retreat.

December

December 1

The Ford Motor Company introduces the first moving assembly line, reducing chassis assembly time from 12½ hours in October to 2 hours, 40 minutes. Although Ford is not the first to use an assembly line, his successful adoption of one sparks an era of mass production.

Crete, having obtained self rule from Turkey after the first Balkan War, is annexed by Greece.

December 12 – Vincenzo Perugia tries to sell the Mona Lisa in Florence and is arrested.